Mathematical abstraction refers to the abstraction of quantitative relations and spatial forms in order to obtain the literacy of mathematical research objects. It mainly includes: abstracting the relationship between mathematical concepts and concepts from the relationship between quantity and shape, abstracting general laws and structures from the specific background of things, and expressing them in mathematical language.
Logical reasoning refers to the completion of deducing other propositions or conclusions from some facts and propositions according to rules. It mainly includes two categories: one is reasoning from special to general, and the main forms of reasoning are induction and analogy; One is from general to special reasoning, and the main form of reasoning is deduction.
Mathematical modeling is the result of mathematical abstraction of real problems, expression of problems in mathematical language and establishment of models to solve problems in mathematical methods. The process of mathematical modeling mainly includes: finding problems, putting forward problems, analyzing problems, establishing models, determining parameters, calculating solutions, testing results, improving models, and finally solving practical problems.
Intuitive imagination refers to the quality of perceiving the changes of things' forms with the help of geometric intuition and spatial imagination, and using spatial forms, especially graphics, to understand and solve problems. It mainly includes: understanding the positional relationship, morphological change and motion law of things with the help of spatial form.
Mathematical operation refers to solving problems according to the algorithm on the basis of defining the object of operation. It mainly includes: understanding the operation object, mastering the algorithm, exploring the operation idea, selecting the operation method, designing the operation program to obtain the operation result, etc.
Data analysis refers to obtaining data from the research object, sorting, analyzing and inferring the data by mathematical methods, and forming knowledge literacy about the research object. The process of data analysis mainly includes: collecting data, sorting out data, extracting information, establishing models and drawing conclusions.
The benefits of learning mathematics
People who are good at math are relatively smart and savvy, and they can show their advantages in dealing with people. The faster you think, the more ways and ideas you have. Cambridge, majoring in financial mathematics at Carnegie Mellon University in the United States, said that studying mathematics has brought her mental exercise and made me pay more attention to the rigor of thinking in my life.
For example, before solving a problem, I like to divide it into several sections, and each section is divided into several steps, so that I can dig slowly like a branch instead of thinking in confusion in front of a pile of data. Mathematics is the foundation of other disciplines, and it is easier for people who learn mathematics well to get into other disciplines. Learning software, computer, finance and other engineering majors is even more handy.
Can manage money better than others. The application of mathematics in life is everywhere. Nowadays, the society is already an information society, and mathematical knowledge is used in financial management and computers. Warren Buffett is very powerful, but Buffett's power is also based on mathematics. Buffett's decision-making process is actually the method of using subjective probability.